joe s: I used plain ol Weaver style rings, whoever makes them, but the ones using the allen screw rather than the slotted screws - they seem to hold better. I also use a little locktite to dampen vibration in/on the screw threads.
Real world ballistics for both the 240 gn and the Hornaday 265 gn Light Magnum are about the same from your 20" bbl, somewhere around 2300'/sec, and that is plenty for those weight slugs. With factory 240s, if sight in for 1" high at 100 yds, you will be about that at 50 yds and about an inch or so low at 150. You will be close to 2-3" low at 200 yds.
Firelapping improves the accuracy of all bullets, at least in my rifles and pistols, regardless of the bullet used. Jacketed bullets have responded as favorably as the cast bullets have. After you have purchased, scoped and shot that beast, even if you plan on staying with jacketed bullets either the 240 or the 265 will work very well on either of the critters you mentioned.
I last hunted in South Carolina 30 years ago. We hunted whitetail and hog in one of the game managment areas near the coast. I took two large hogs (380 and 380-something) pounds with my Marlin with a 24" bbl - I used handloads with the 265 gn Hornaday bullet and never had a problem. My preference for the past few years however, coupled with my feeling that the 444 really performs with heavy hard-cast slugs, has been for the cast, gas-checked bullets from Beartooth. Excellent stuff. HTH. Mikey.